Solve: (√2 × √4)/(√144 + √16) - Square Root Fraction Simplification

To solve this problem, let's follow these detailed steps:

The given expression is:
$\frac{\sqrt{2}\cdot\sqrt{4}}{\sqrt{144}+\sqrt{16}}$

Step 1: Simplify the numerator.

In the numerator, we have $\sqrt{2} \cdot \sqrt{4}$. Using the property of square roots, $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$, we can write:

• $\sqrt{2} \cdot \sqrt{4} = \sqrt{2 \cdot 4} = \sqrt{8}$

We can simplify $\sqrt{8}$ further:

• $\sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}$

Step 2: Simplify the denominator.

In the denominator, we have $\sqrt{144} + \sqrt{16}$. Let's compute each square root:

• $\sqrt{144} = 12$ because $12^2 = 144$
• $\sqrt{16} = 4$ because $4^2 = 16$

Thus, the denominator becomes:

• $12 + 4 = 16$

Step 3: Form the fraction and simplify it.

Replacing the simplified numerator and denominator, the expression becomes:

• $\frac{2\sqrt{2}}{16}$

Simplifying the fraction, divide both terms in the fraction by 2:

• $\frac{2\sqrt{2}}{16} = \frac{\sqrt{2}}{8}$

Therefore, the solution to the problem is:

$\frac{\sqrt{2}}{8}$